doc: var_estimation (new), var_model (modify), var_forecast (modify)
Houtan Bastani
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doc/dynare.texi
182
doc/dynare.texi
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@ -215,6 +215,7 @@ The Model file
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* Optimal policy::
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* Sensitivity and identification analysis::
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* Markov-switching SBVAR::
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* Vector Autoregression::
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* Displaying and saving results::
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* Macro-processing language::
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* Verbatim inclusion::
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@ -268,6 +269,11 @@ Types of analysis and output files
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* Screening Analysis::
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* Identification Analysis::
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Vector Autoregression
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* Estimation::
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* Forecasting::
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Macro-processing language
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* Macro expressions::
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@ -1077,7 +1083,7 @@ end of line one and the parser would continue processing.
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* Optimal policy::
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* Sensitivity and identification analysis::
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* Markov-switching SBVAR::
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* Forecast from VARs::
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* Vector Autoregression::
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* Displaying and saving results::
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* Macro-processing language::
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* Verbatim inclusion::
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@ -10207,36 +10213,180 @@ Do not output percentile error bands (@i{i.e.} compute mean). Default:
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@end deffn
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@node Forecast from VARs
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@section Forecast from VARs
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Dynare allows you to include forecasts from VARs in the @ref{Model
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declaration}. A VAR model must be specified using the @ref{var_model} command
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so it may then be used inside the model block via the @ref{var_expectation}
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operator.
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@node Vector Autoregression
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@section Vector Autoregression
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Dynare allows you to estimate VAR models and to use forecasts from those VARs in the @ref{Model
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declaration}. A VAR model must be specified using the @ref{var_model} command.
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@anchor{var_model}
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@deffn Command var_model (var_model = @var{FILENAME}, var_order = @var{INTEGER}) @var{VARIABLE_NAME} [@var{VARIABLE_NAME}@dots{}];
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@deffn Command var_model (@var{OPTIONS}@dots{}) @var{VARIABLE_NAME} [@var{VARIABLE_NAME}@dots{}];
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@descriptionhead
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This declares a VAR model whose forecast can be used in the model block.
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This declares a VAR model that can be estimated and/or whose forecast can be used
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in the model block.
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The @code{var_model} specifier must be passed to the command as it specifies
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the name of the @code{.mat} file that contains the estimatied intercepts and
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coefficient matricies of the VAR. The intercept must be specified in a variable
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called @code{mu} and the coefficients must be specified in a cell array called
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The @code{var_model} command depends on a data file, specified either by the
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@code{model_name} option or the @code{datafile} option (see below). In the data
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file, the intercept must be stored in a variable called @code{mu} and the
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coefficients must be stored in a cell array called
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@code{autoregressive_matrices}. If the command specifies a VAR of order
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@code{p} with @code{n} endogenous variables, then @code{mu} will be an @code{n}
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by @code{1} array and @code{autoregressive_matricies} will have @code{p} cells,
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each containing an @code{n} by @code{n} matrix.
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The @code{var_order} specifier must be passed to the command as it specifies
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the lag length of the VAR.
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The @ref{var_model} command must be followed by a list of endogenous variables,
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which are the variables of the VAR.
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@optionshead
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@table @code
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@anchor{var_model_model_name}
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@item model_name = @var{VARIABLE_NAME}
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The name of the VAR model. By default, it specifies the name of the @code{.mat}
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file that contains the estimatied intercepts and coefficient matricies of the
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VAR. This option is required.
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@item datafile = @var{FILENAME}
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By default, the data is contained in @code{<<model_name>>.mat}. If the data for
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estimation is contained in a different file, you can pass the filename to this
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option.
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@item order = @var{INTEGER}
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The number of lags in the VAR. Default: @code{1}
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@end table
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@end deffn
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@menu
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* Estimation::
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* Forecasting::
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@end menu
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@node Estimation
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@subsection VAR Estimation
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To estimate a VAR it must first be declared via the @ref{var_model}
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command. Then it is the @code{var_estimation} command that launches LS
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estimation.
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@anchor{var_estimation}
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@deffn Command var_estimation (@var{OPTIONS}@dots{});
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@descriptionhead
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This declares a VAR model that can be estimated and/or whose forecast can be used
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in the model block.
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The @ref{var_model} command must be followed by a list of endogenous variables,
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which are the variables of the VAR.
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@optionshead
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@table @code
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@item model_name = @var{VARIABLE_NAME}
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The name of the model to be estimated, previously declared via the
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@ref{var_model} command. This is a required argument.
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@item datafile = @var{FILENAME}
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By default, the data is contained in @code{<<model_name>>.mat}. If the data for
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estimation is contained in a different file, you can pass the filename to this
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option.
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@end table
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@end deffn
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@deffn Block restrictions (@var{VARIABLE_NAME});
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@descriptionhead
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The @code{restrictions} block allows you to impose constraints on the VAR to
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be estimated.
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The block takes a @var{VARIABLE_NAME} argument which refers to the VAR model to which
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the restrictions apply (as specified by @ref{var_model_model_name}).
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The VAR constraints are written in a block delimited by @code{restrictions} and
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@code{end} keywords.
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@b{Exclusion Restrictions} can be imposed with a main line indicating the lag
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at which the exclusion restriction should apply:
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@example
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EXCLUSION LAG @var{INTEGER};
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@end example
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All subsequent lines will be applied at the specified lag and look like:
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@example
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EQUATION (@var{VARIABLE_NAME}) @var{VARIABLE_NAME} [@var{VARIABLE_NAME}@dots{}];
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@end example
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Here, the @var{VARIABLE_NAME} between parenthesis specifies the equation from
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which the following @var{VARIABLE_NAME}(s) will be excluded (again, at the
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specified lag).
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A concrete example could be helpful. In a VAR(3) with variables @code{a},
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@code{b}, and @code{c}, we could exclude @code{b} and @code{c} at lag @math{2}
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from the equation where @code{a} is the independent variable, and exclude
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@code{c} at lags @math{2} and @math{3} from @code{b}'s equation by including
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the following the @code{.mod} file:
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@example
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restrictions(my_var_model);
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exclusion lag 2;
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equation(a) b c;
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equation(b) c;
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exclusion lag 3;
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equation(b) c;
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end;
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@end example
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@anchor{restriction_equation}
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@b{Linear Restrictions in an Equation} of the form @math{C\beta=c} can be imposed with a line in the form of:
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@example
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RESTRICTION EQUATION (@var{VARIABLE_NAME}) ...
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COEFF(@var{VARIABLE_NAME}, @var{INTEGER}) [*|/] @var{EXPRESSION} ...
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[[+|-] COEFF(@var{VARIABLE_NAME}, @var{INTEGER}) [*|/] @var{EXPRESSION}] = @var{DOUBLE};
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@end example
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Here, the first @var{VARIABLE_NAME} is the equation to which this restriction
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applies. @code{COEFF(@var{VARIABLE_NAME}, @var{INTEGER})} means the coefficient
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on @var{VARIABLE_NAME} at lag @var{INTEGER} to which this relation applies. The
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coefficient is either multiplied or divided by an @var{EXPRESSION}. The
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constraint can be additive or subtractive with another coefficient in the same
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equation. All of this is set equal to a constant value, @var{DOUBLE}.
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@b{Linear Restrictions accross Equations} can be imposed with a line in the form of:
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@example
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RESTRICTION CROSSEQUATIONS ...
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COEFF(@var{VARIABLE_NAME}, @var{VARIABLE_NAME}, @var{INTEGER}) [*|/] @var{EXPRESSION} ...
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[[+|-] COEFF(@var{VARIABLE_NAME}, @var{VARIABLE_NAME}, @var{INTEGER}) [*|/] @var{EXPRESSION}] ...
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= @var{DOUBLE};
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@end example
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Same as for @ref{restriction_equation}. The only difference being the
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@code{COEFF} operator takes three arguments. The first specifies the equation
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on which the coefficient on the second argument should be applied. The lag at
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which it is applied is the third argument.
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@b{Covariance Matrix Exclusion Restrictions} can be imposed with a line in the form of:
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@example
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RESTRICTION COVARIANCE (@var{VARIABLE_NAME}, @var{VARIABLE_NAME}) = 0;
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@end example
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which says that the covariance between the two variables is zero.
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@b{Covariance Matrix Restrictions} can be imposed with a line in the form of:
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@example
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RESTRICTION COVARIANCE (@var{VARIABLE_NAME}, @var{VARIABLE_NAME}) = ...
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(@var{VARIABLE_NAME}, @var{VARIABLE_NAME});
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@end example
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which says that the covariance between the two pairs of variables is equal.
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@end deffn
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@node Forecasting
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@subsection VAR Forecasts
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To use a forecast from a VAR in the @code{model} block, it must first be
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declared via the @ref{var_model} command. It can then be used in the
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@code{model} block using the @ref{var_expectation} operator.
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@node Displaying and saving results
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@section Displaying and saving results
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